APRIL 29, 2021
WHICH CAME FIRST, the chicken or the egg? As the authors of Reimagining Time make clear, one of the most important conceptual advances of the 20th century was to note that we cannot lose sleep over philosophical questions like this until we have nailed down what it means for two things to occur simultaneously, never mind for one thing to occur before the other. And it was the crucial insight of a Swiss patent clerk named Albert Einstein that the simultaneity of two events — not to mention the passage of time, and even the physical dimensions of objects — was actually relative to the frame of reference of the observer. This overthrew a good 250-odd years of scientific consensus regarding the Newtonian structure of the space and time and still remains something of an intellectual challenge for the uninitiated. It is the purpose of this book, an imaginative collaboration between a graphic artist and a professional physicist, to help us get the underlying principles straight.
Of course, ever since the 1905 publication of his article “On the Electrodynamics of Moving Bodies,” there have been no shortage of attempts to grapple with and explicate the central ideas of Einstein’s theory of relativity. Many physicists initially dismissed the paper as a rather modest contribution to an already well-established field, not least because the central mathematical principles involved — called the Lorentz-FitzGerald transformations — were already in common currency. The identification of light as an electromagnetic wave had naturally raised questions about the so-called luminiferous ether through which it was supposed to propagate, and so numerous experimental attempts were made to detect it. The failure of the famous Michelson-Morley experiments in 1888 spawned ever more baroque attempts to refine the concept of the ether and to explain why it so stubbornly refused detection, systematically distorting, as it were, any measuring devices. Einstein’s proposal that the ether be abandoned outright — and that we instead take the speed of light to be a constant in all frames of reference — was another method for reconciling these experimental results, one that proposed applying the Lorentz-FitzGerald transformations not to our measuring devices, but to the structure of time and space itself. It was an elegant proposal, although conceptually more radical, and few took it seriously.
Over a century later, and the situation is almost entirely reversed. Reimagining Time takes for granted that the speed of light is a constant — a scientific truth now firmly embedded in the popular imagination — and then seeks to tease out what exactly this means. There is thus no attempt to convince us of the comparative economy of Einstein’s key insight over its rival ether theories, no discussion of the later development in 1915 of a general theory capable of accommodating accelerated motion, and no mention of the carefully orchestrated Eddington expedition of 1919 that made the theory of relativity front-page news. No one needs to be convinced anymore that Einstein was right — they just need to know what he was right about.
We are thus spared almost any theory at all; there is no attempt — as one of the authors put it — “to plug numbers into equations I didn’t really understand, thereby turning them into other numbers I didn’t really understand.” The first sections of the book require nothing more taxing than halving or doubling the length of a train car traversed by a beam of light. The latter sections, which introduce the effects of time dilation and length contraction, involve a few more numbers, although mainly for comparative purposes, as the underlying principles are presented purely in qualitative terms. And while the final part of the book asks us to bear in mind that momentum is the product of mass and velocity, and is preserved during a collision, at no point are we required to do more than add and subtract a few values. The illustrations are also good — clear and uncluttered, and peopled with friendly looking figures channeling the reader’s bemusement at the behavior of light — and although the book does not exactly break the mold in depicting various observers on moving trains firing light-beams at one another, they certainly are helpful devices. That even the most counterintuitive consequences of the theory of relativity can be so easily drawn out with a handful of simple illustrations is itself revealing, not merely of the deft touch of the authors, but of the deep roots the theory has now taken in our culture.
Reimagining Time proceeds step-by-step, slowly teasing out one implication at a time. If light only ever goes at one speed, then you can never catch up with a light-beam fired from your trusty laser — and by the same token, you can never out-run a light-beam either, for no matter how fast you go, it will always keep coming after you at the same rate, like the shambling horror in some old black-and-white movie. It also means that if one observer fires off a light-beam in tandem with another observer passing by on a faster moving train, the two of them are going to come to some very different conclusions about time and space. If light only ever goes at one speed, then both observers will observe the two light-beams shooting off together in perfect lock-step, since no light-beam can ever overtake another. From the perspective of the stationary observer, by the time these two light-beams have reached the end of his train, they will only have made it part way across the faster moving train of their counterpart. But since light only ever goes at one speed, it is also the case that this other observer has not in any way managed to catch up with their own light-beam. Instead, less time must have passed for the faster moving observer, as this is the only other way that we can accommodate the fact that the two light-beams have only made it part way across their train. And of course, what applies for one observer will also apply in reverse, since it is all a matter of perspective as to which of these two observers we consider to be at rest, and which in motion.
Once we are happy with the fact that time has to vary to accommodate the constant speed of light, the next step is to illustrate how this leads directly to the relativity of simultaneity, and from there to the relativity of spatial distance. Here we are playfully invited to hold up one thumb and scroll the illustrations in the book from side-to-side to replicate the passage of our train-bound observers, and to grasp that if light only ever goes at one speed, the same light-beams emitted from the center of the page will first spill out from different edges depending upon our motion relative to the book. From there, it is a short step to mark the occurrence of these events on the side of our passing trains, and to see that if different observers come to different conclusions about the length of time that passes between two events, they must also come to different conclusions about the spatial distance separating these recorded marks.
And it is here that the predominantly qualitative approach of Reimagining Time is particularly effective. Many introductions to the relativity of simultaneity will begin with a philosophical detour through the problems of measurement, and the issues involved in transporting carefully synchronized clocks from one location to another for the purposes of comparison — important prerequisites for a thorough grasp of the mechanics of the situation, but one that threatens to distract from the underlying point. Moreover, such a focus can also encourage a misleadingly operationalist understanding of the principles involved, as happened with many of Einstein’s contemporaries working in the philosophical climate of the early 20th century. Bad philosophy often leads to even worse politics, and it was the vague suspicion that physics had somehow become a matter of convention or taste that motivated many of the more absurd responses to relativity in the early half of the 20th century. Writing to his friend and collaborator Marcel Grossmann in 1920, Einstein remarked that: “The world is a strange madhouse. Currently, every coachman and every waiter is debating whether relativity theory is correct. Belief in this matter depends on political party affiliation.”
In the same year, the racially unambiguous Association of German Natural Scientists for the Preservation of Pure Science had packed the Berlin Concert Hall with a sell-out conference denouncing the political motivations behind the theory of relativity; in the 1930s and 1940s, Soviet scientists debated whether relaxing the underlying structure of space-time helped or hindered the proletariat revolution. Such issues seem absurd now, as we ride our trains and fire light-beams at passing observers, comfortably secure in the principles of relativity even if we don’t always know what they are.
The final sections of Reimagining Time are by necessity a little more challenging. In order to give a sense of the extent to which time dilates and length contracts, our laser-toting train commuters have to fire their light-beams in both the vertical and horizontal axes. This generates the triangular space-time diagrams familiar from the more usual introductions — although fortunately we are not invited to use “a little high-school trigonometry” to derive the Lorentz-FitzGerald factor. Rather, we are presented with a range of simple ratios and fractions sufficient to appreciate the underlying result, with the mathematical heavy lifting confined to the appendix. All of this comes together in the exchange rate of mass and energy, the only section of the book where we need to add and subtract a few numbers in order to maintain the conservation of momentum. It is notable again that the well-known mass-energy equivalence E=mc2 is also merely stated as an incontestable fact — another of those well-known scientific truths that has now fully permeated popular culture, something that needs to be explicated rather than derived afresh.
Reimagining Time ends with its own variation on the infamous twin paradox. Rapidly hatching eggs are passed back and forth between our train-traveling observers who, due to the effects of time dilation, come to very different judgments as to when these various chickens hatch. Although this does not delve into the full version of the paradox — which requires the change in inertial motion only accommodated by the general theory of relativity — it is a satisfying way to bring the various aspects of the foregoing discussion together. It is also presumably a deliberate setup for any reviewer to crack wise about the relative priority of the chicken and the egg, and to conclude that it all depends upon whether the chicken was crossing the road (and at what fraction of the speed of the light it was moving). But after finishing this charming and genuinely informative introduction to the principles of relativity, one cannot help but want to play along.
Paul Dicken received a PhD in the history and philosophy of science from Cambridge. He is the author of A Critical Introduction to Scientific Realism (Bloomsbury) and Getting Science Wrong (Bloomsbury). He also writes short fiction.